Think of 'entering' a state as crossing the boundary between the outside into the box that corresponds to the new state. Or even more concrete, think of a state 'InsideTheHouse', and entering that state as going through some door. You need to enter before you are actually in the new state, just as you have to pass the door, in order to get to the actual state of 'InsideTheHouse'.

This is a quite general pattern used by any state machine implementation I ever came across. I'm not entirely sure though whether the default texts about software patterns explain this very clearly though, as it really is more of an implementation detail than a generic pattern.